The results we present in FIG. REF -REF  correspond to the exact Gibbs sampling taken according to Eq. (REF )-(REF ). The massively parallel architecture we present updates p-bits in parallel while ensuring every single update is made with the latest network state, as required by Gibbs sampling. In the present examples, the exact Gibbs sampling requirement resulted in 15 MHz clocks, dictated by the neighbor distribution of p-bits and the adder delays in the hardware. Next, we tested whether overclocking, namely using faster than 15 MHz clocks improves performance or not (FIG. REF a). We define overclocking such that at least some of the updates are not made based on the latest state of the network, similar in spirit to message passing algorithms [1]} or the Hogwild!-Gibbs sampling algorithm [2]}.
